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arXiv · 1310.2515

Tracy-Widom asymptotics for q-TASEP

Patrik L. Ferrari·Balint Veto
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Abstract

We consider the q-TASEP that is a q-deformation of the totally asymmetric simple exclusion process (TASEP) on Z for q in [0,1) where the jump rates depend on the gap to the next particle. For step initial condition, we prove that the current fluctuation of q-TASEP at time t are of order t^{1/3} and asymptotically distributed as the GUE Tracy-Widom distribution, which confirms the KPZ scaling theory conjecture.

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Patrik L. Ferrari, Balint Veto. 2013-10-09. Tracy-Widom asymptotics for q-TASEP. https://doi.org/10.1214/14-aihp614

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